CN113114343A - High-energy-efficiency intelligent dynamic beam forming method for multi-beam satellite - Google Patents

High-energy-efficiency intelligent dynamic beam forming method for multi-beam satellite Download PDF

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CN113114343A
CN113114343A CN202110387140.9A CN202110387140A CN113114343A CN 113114343 A CN113114343 A CN 113114343A CN 202110387140 A CN202110387140 A CN 202110387140A CN 113114343 A CN113114343 A CN 113114343A
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satellite
optimization problem
optimal solution
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CN113114343B (en
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伍诗语
田佳辰
姚志伟
凌泰炀
季书鹏
刘彦浩
王闻今
李潇
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Southeast University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/14—Relay systems
    • H04B7/15—Active relay systems
    • H04B7/185—Space-based or airborne stations; Stations for satellite systems
    • H04B7/18578—Satellite systems for providing broadband data service to individual earth stations
    • H04B7/18586—Arrangements for data transporting, e.g. for an end to end data transport or check
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/045—Combinations of networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0426—Power distribution
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/18—TPC being performed according to specific parameters
    • H04W52/24—TPC being performed according to specific parameters using SIR [Signal to Interference Ratio] or other wireless path parameters
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/18—TPC being performed according to specific parameters
    • H04W52/26—TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service]
    • H04W52/265—TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service] taking into account the quality of service QoS
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
    • H04W16/24—Cell structures
    • H04W16/28—Cell structures using beam steering

Abstract

The invention provides an energy-efficient intelligent dynamic beam forming method suitable for a multi-beam satellite, which is used for a satellite mobile communication system, firstly, the energy efficiency problem of the satellite mobile communication system is modeled, and the dynamic beam forming method is designed into a dynamic beam optimization problem with minimum power consumption required by the satellite system for transmitting each bit of information; and then, a semi-positive definite relaxation method is utilized, and a Minorize-Maximization iterative algorithm is combined to solve the convex programming difference problem, then, the objective function is further converted into a standard convex optimization problem through quadratic transformation, and iterative solution is carried out to obtain the optimal solution under the semi-positive definite relaxation condition. If the solution rank is not one, power redistribution is carried out by adopting a Gaussian randomization method, and finally a dynamic beam forming vector meeting the rank-one condition is obtained, and in the process of power redistribution, an objective function needs to be converted into a convex optimization problem to be solved by using the same method.

Description

High-energy-efficiency intelligent dynamic beam forming method for multi-beam satellite
Technical Field
The invention belongs to the field of communication, and particularly relates to an energy-efficient intelligent dynamic beam forming method suitable for a multi-beam satellite communication system.
Background
With the increasing demand for data rates in satellite communication systems, the multi-beam system framework has become a trend. The traditional multi-beam communication system adopts a fixed multi-beam coverage technology, and the spot beams adopt a seamless coverage of a complete whole area of a cellular structure, so that the traditional coverage mode has the defects of low resource utilization efficiency and the like in view of relatively few active users of a satellite system in an actual communication scene. Therefore, dynamic multi-beam coverage techniques are gradually gaining attention and research. In the dynamic multi-beam satellite system, the idea that one beam serves one user is provided, and the coverage mode is a user-centered service mechanism, so that the signal quality of the user can be effectively improved.
In addition, as the concept of sustainable development and pursuit of green communication is increasingly emphasized, energy efficiency has become an important consideration in satellite communication. Satellites are generally powered by solar panels, and therefore, a trend of satellite communication systems to pursue high energy efficiency and low power consumption has been.
In addition, the rapid development of the deep learning algorithm, the increase of mass data acquisition channels and the remarkable improvement of hardware calculation and storage capacity enable artificial intelligence to be developed explosively in recent years.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide an energy-efficient intelligent dynamic beam forming method of a multi-beam satellite communication system.
The technical scheme is as follows:
the invention relates to an energy-efficient intelligent dynamic beam forming method of a multi-beam satellite communication system, which comprises the following steps:
(1) analyzing a channel of a downlink of satellite communication, and representing a channel response vector transmitted to each user by the phased array antenna by considering Doppler frequency shift and propagation delay;
(2) taking the energy efficiency maximization of the system as a target, and taking the total energy consumption of the satellite communication system divided by the sum of the information rates of the users as a target function;
(3) establishing an energy-efficient dynamic beam optimization design problem, and taking the guarantee of the service quality of each user and the power limit of each sub-antenna of the phased array antenna as constraint conditions;
(4) solving a convex programming difference problem by using a semi-positive definite relaxation method and combining a Minorize-Maximization iterative algorithm, then further converting an objective function into a standard convex optimization problem through quadratic transformation, and solving the problem in an iterative manner to obtain an optimal solution under the semi-positive definite relaxation condition;
(5) if the rank of the optimal solution matrix is one, a dynamic beam forming vector can be directly obtained; if not, carrying out power redistribution by using Gaussian randomization to obtain a final forming vector;
(6) in the optimization process of power redistribution, a deep learning technology is introduced, a convolutional neural network is built, input parameters are the optimal solution of a channel autocorrelation matrix and a semi-positive definite relaxation condition, the distributed power is output, and an iterative process is replaced through the mapping relation between the input parameters and the optimal solution.
Preferably, the channel response transmitted by the phased array antenna to user k in step (1) can be expressed as:
Figure BDA0003011303190000021
wherein, therein
Figure BDA0003011303190000022
Due to the doppler shift caused by the satellite movement,
Figure BDA0003011303190000023
for propagation delay, gkIs the coefficient of the gain of the channel,
Figure BDA0003011303190000024
is the downlink response vector of the phased array antenna.
Preferably, in step (2), the objective function is established as
Figure BDA0003011303190000025
Wherein R issumSum of information rates for K users, PsumTotal energy consumption, P, for low-earth satellite systems0Representing the basic power consumption, w, of each userkRepresents the power vector of the phased array antenna to the kth user, the superscript H represents the conjugate transpose, xi represents the constant of the inefficiency of the power amplifier and xi > 1,
Figure BDA0003011303190000026
for the received sir for the kth user in the downlink transmission,
Figure BDA0003011303190000027
the variance of the noise received for the kth user.
Preferably, the optimization problem established in step (3) can be expressed as
Figure BDA0003011303190000028
Wherein P isnFor maximum allowed transmit power for a single antenna, gammakIs the target signal-to-interference-and-noise ratio of the kth user, K is the total number of users, NT＝Mx×MyNumber of antennas of satellite antenna array, MxAnd MyThe numbers of the x-axis and the y-axis in the antenna array are respectively, and n represents the serial number of the sub-antenna in the antenna array.
Preferably, the method for solving the optimization problem in step (4) includes:
a. using semi-positive definite relaxation, define hkThe autocorrelation matrix is
Figure BDA0003011303190000031
wkThe autocorrelation matrix is
Figure BDA0003011303190000032
wiThe autocorrelation matrix is
Figure BDA0003011303190000033
Transforming optimization problems into
Figure BDA0003011303190000034
Where Tr (-) represents a trace of the matrix.
b. The numerator of the above partial formula is represented by A (W), and the denominator is represented by B (W). The molecular fraction a (w) was decomposed according to the log function properties to yield:
Figure BDA0003011303190000035
Figure BDA0003011303190000036
both with respect to WkThe concave function of (A) and (W) is converted into a concave function by utilizing a Minorize-Maximization iterative algorithm according to the characteristics of a convex programming difference problem：
Figure BDA0003011303190000037
c. Then, carrying out secondary transformation on the whole fraction, and converting the problem into a standard convex optimization problem:
Figure BDA0003011303190000038
and solving the convex optimization problem with the initial feasible point, continuing iteration for the next time, converting the problem into an iterative optimization problem, and solving an optimal solution.
Preferably, the power redistribution using the gaussian randomization method in step (5) comprises:
a. if the rank of the optimal solution is one, performing eigenvalue decomposition on the solved optimal solution matrix to obtain a beam forming vector
Figure BDA0003011303190000041
Wherein v iskAnd ukAre respectively
Figure BDA0003011303190000042
The principal eigenvalues and the eigenvectors of (a).
b. If the rank is not one, converting the optimization problem into a convex optimization problem by using a Minorize-Maximization iterative algorithm again for a plurality of Gaussian randomization processes, and selecting a power distribution vector corresponding to the optimal solution from the obtained Gaussian randomization results to further obtain a final dynamic beam forming vector.
Preferably, in step (6), a convolutional neural network framework is built, which comprises an input layer, a convolutional layer, a batch normalization layer, an activation layer, a flat layer, a full connection layer and an output layer, wherein the input is a channel vector
Figure BDA0003011303190000043
And the optimal solution W under the semi-positive definite relaxation conditionoptSplitting a channel vector into a real part and an imaginary part as input;outputting the distributed power p, namely obtaining the mapping relation which can be expressed as
Figure BDA0003011303190000044
Therefore, an iterative process can be replaced, and a final dynamic beam forming vector is obtained.
Has the advantages that: the invention provides an energy-efficient intelligent dynamic beam forming method of a multi-beam satellite communication system, which researches an efficient resource allocation method capable of meeting the service quality of a user by establishing an energy-efficient dynamic beam optimization design problem, introduces artificial intelligence to reduce the calculation amount and has lower operation complexity.
Drawings
Figure 1 is a schematic diagram of a multi-beam satellite mobile communications system;
FIG. 2 is a general flow diagram of the method of the present invention;
FIG. 3 is a detailed method flowchart of an embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings in which:
the embodiment of the invention provides an energy-efficient intelligent dynamic beam forming method of a multi-beam satellite, and figure 1 is a system configuration schematic diagram, and a satellite side is provided with NT＝Mx×MyArea array antenna, MxAnd MyThe number of x-axis and y-axis in the antenna array, respectively, NTEach beam serves K users simultaneously, each user receiving for a single antenna. FIG. 2 is a flow chart of an algorithm, in which the method first considers modeling the energy efficiency problem and designs a dynamic beam optimization problem with minimum power consumption for transmitting each bit of information by a satellite system; then the semipositive relaxation method is utilized and Mi is combinedAnd if the rank of the solution is not one, performing power redistribution by adopting a Gaussian randomization method to finally obtain a dynamic beam forming vector meeting the rank one condition. In the process of power redistribution, an objective function needs to be converted into a convex optimization problem to be solved by the same method, a deep learning method is adopted in the process, a convolutional neural network is established to further replace an iterative process, input parameters are an optimal solution under the conditions of a channel autocorrelation matrix and semi-positive definite relaxation, the distributed power is output, a mapping relation between the channel autocorrelation matrix and the optimal solution is established to replace the iterative process of an optimization algorithm, and the calculation complexity is reduced. The detailed steps are shown in fig. 3, and specifically are as follows:
(1) the channel transmitted by the phased array antenna of the satellite to user k is modeled as:
Figure BDA0003011303190000051
wherein
Figure BDA0003011303190000052
Due to the doppler shift caused by the satellite movement,
Figure BDA0003011303190000053
for propagation delay, it is assumed here that the channel gain factor gkObeying a Rice factor of κkHas a fading distribution of lais and power
Figure BDA0003011303190000054
Equivalently, the channel gain factor gkSubject to mean values of real and imaginary parts, respectively
Figure BDA0003011303190000055
Variance of
Figure BDA0003011303190000056
A real gaussian distribution.
Figure BDA0003011303190000057
For the downlink response vector of a phased array antenna,
Figure BDA00030113031900000512
representing the kronecker product, the array angular response vector in the x-direction is
Figure BDA0003011303190000058
Similarly, the array angular response vector in the y-direction is
Figure BDA0003011303190000059
In the formula, MxAnd MyThe number of x-axis and y-axis in the antenna array, and the direction cosine quantity
Figure BDA00030113031900000510
Figure BDA00030113031900000511
(2) The present invention aims to achieve the objective of minimizing the total energy consumption required by a satellite system to transmit each bit of information, and can be expressed in mathematical form as:
Figure BDA0003011303190000061
wherein R issumSum of information rates for K users, PsumFor the total energy consumption of the satellite system, P0Representing the basic power consumption, w, of each userkRepresents the power vector of the phased array antenna to the kth user, the superscript H represents the conjugate transpose, xi represents the constant of the inefficiency of the power amplifier and xi > 1,
Figure BDA0003011303190000062
for the received sir for the kth user in the downlink transmission,
Figure BDA0003011303190000063
the variance of the noise received for the kth user.
(3) Expressing the optimization problem as the minimum energy required by the satellite system for transmitting each bit of information, and enabling the signal-to-interference-and-noise ratio transmitted to each user to be larger than a certain set threshold value, so that the service quality of each user can be guaranteed in the transmission process of the system; meanwhile, the transmitting power of each sub-antenna in the phased array antenna is restrained, so that the phased array antenna works in a linear area, the nonlinear distortion caused by overload of the antenna is avoided, and the specific problem is expressed as follows:
Figure BDA0003011303190000064
wherein P isnFor maximum allowed transmit power for a single antenna, gammakIs the target signal-to-interference-and-noise ratio of the kth user, K is the total number of users, NT＝Mx×MyNumber of antennas of satellite antenna array, MxAnd MyThe numbers of the x-axis and the y-axis in the antenna array are respectively, and n represents the serial number of the sub-antenna in the antenna array.
In order to solve the above problem by converting it into a convex problem, the objective function of the above problem is first changed from minimizing the transmitted power per bit to maximizing the energy efficiency of the system, i.e., the power efficiency of the system is maximized
Figure BDA0003011303190000065
That is, the objective function can be converted to:
Figure BDA0003011303190000071
(4) iterative by hemipositive relaxation in combination with Minorize-maxinizationThe algorithm converts the convex optimization problem into a convex optimization problem to be solved. First consider a semi-positive definite relaxation, defining hkThe autocorrelation matrix is
Figure BDA0003011303190000072
wkThe autocorrelation matrix is
Figure BDA0003011303190000073
After neglecting rank-one constraint rank (W)k) In the case of 1, i.e. under semi-positive relaxation conditions, problem Q2Can be converted into:
Figure BDA0003011303190000074
where Tr (-) represents a trace of the matrix. The fractional objective function being with respect to the variable WkFirst, the molecule is divided into
Figure BDA0003011303190000075
The female part is
Figure BDA0003011303190000076
The molecular fraction a (w) was decomposed according to the log function properties to yield:
Figure BDA0003011303190000077
order to
Figure BDA0003011303190000078
Both with respect to WkThe g (w) function is linearized with taylor expansions by the miniize-Maximization iterative algorithm, so that a (w) is converted into a concave function. A (W) can be approximated as:
Figure BDA0003011303190000079
where t denotes the number of iterations, partial derivatives
Figure BDA0003011303190000081
At this time, the objective function
Figure BDA0003011303190000082
The numerator of (2) is a concave function, the denominator is a linear function, the condition of quadratic transformation is satisfied, the quadratic transformation is adopted for the following bisection formula, and the objective function is further transformed, namely:
Figure BDA0003011303190000083
wherein the auxiliary variables are defined as:
Figure BDA0003011303190000084
the auxiliary variable y is updated at each iteration. So that the original problem is changed into a convex optimization problem in the form of
Figure BDA0003011303190000085
Problem Q4For the standard convex problem, the method can be used for solving by using a conventional convex optimization method or other iterative algorithms to obtain the optimal solution under the semidefinite relaxation
Figure BDA0003011303190000086
(5) After the optimal solution of the problem is obtained according to the step (4), if
Figure BDA0003011303190000087
If the rank of (D) is not unique, power redistribution is performed by using a Gaussian randomization method
Figure BDA0003011303190000088
By means of the gaussian randomization,further obtaining an optimal solution meeting the rank condition, namely:
Figure BDA0003011303190000089
and (5) carrying out convex transformation on the target function, wherein the numerator part is A (p) and the denominator part is B (p) in the same way. Likewise, one can obtain:
Figure BDA0003011303190000091
order to
Figure BDA0003011303190000092
Then converting A (p) into concave function. A (p) can be approximated as:
Figure BDA0003011303190000093
where t denotes the number of iterations, partial derivatives
Figure BDA0003011303190000094
After the auxiliary variable h is introduced, the objective function is converted into:
Figure BDA0003011303190000095
wherein the auxiliary variables are defined as:
Figure BDA0003011303190000096
after G times of Gaussian randomization, a suboptimal dynamic beam forming vector is obtained
Figure BDA0003011303190000097
To obtain the maximum value of the objective function as the final dynamic beamforming vector.
(6) And (4) converting the original problem into a final convex optimization problem, and then obtaining an optimal solution by using an iteration method, wherein in the step, the iteration process is replaced by using a deep learning technology, so that the calculation complexity is reduced, and the algorithm solving speed is accelerated. Firstly, a convolutional neural network framework is built, and the convolutional neural network framework comprises an input layer, a convolutional layer, a batch normalization layer, an activation layer, a flat layer, a full connection layer and an output layer. The inputs to the neural network being channel vectors
Figure BDA0003011303190000098
And the optimal solution W under the semi-positive definite relaxation conditionoptSince the present neural network does not support channel coefficients in complex form, the channel vector is used
Figure BDA0003011303190000099
Are split into
Figure BDA00030113031900000910
And
Figure BDA00030113031900000911
two parts forming a new input
Figure BDA0003011303190000101
Figure BDA0003011303190000102
And
Figure BDA0003011303190000103
is the real and imaginary parts of each corresponding element in h; the input elements are trained in the neural network layer to obtain output, and the output is determined for the allocated power p, namely the mapping relation of the input elements and the allocated power p and expressed as
Figure BDA0003011303190000104
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

Claims (7)

1. An energy-efficient intelligent dynamic beamforming method suitable for a multi-beam satellite is characterized by comprising the following steps:
(1) analyzing a channel of a downlink of satellite communication, and representing a channel response vector transmitted to each user by the phased array antenna by considering Doppler frequency shift and propagation delay;
(2) taking the energy efficiency maximization of the system as a target, and taking the total energy consumption of the satellite communication system divided by the sum of the information rates of the users as a target function;
(3) establishing an energy-efficient dynamic beam optimization design problem, and taking the guarantee of the service quality of each user and the power limit of each sub-antenna of the phased array antenna as constraint conditions;
(4) solving a convex programming difference problem by using a semi-positive definite relaxation method and combining a Minorize-Maximization iterative algorithm, then further converting an objective function into a standard convex optimization problem through quadratic transformation, and solving the problem in an iterative manner to obtain an optimal solution under the semi-positive definite relaxation condition;
(5) if the rank of the optimal solution matrix is one, a dynamic beam forming vector can be directly obtained; if not, carrying out power redistribution by using Gaussian randomization to obtain a final forming vector;
(6) in the optimization process of power redistribution, a deep learning technology is introduced, a convolutional neural network is built, input parameters are the channel response vector of a user and the optimal solution under the semi-positive relaxation condition, the distributed power is output, and the iterative process is replaced through the mapping relation between the distributed power and the optimal solution.
2. The method for energy-efficient intelligent dynamic beamforming for multi-beam satellites according to claim 1, wherein the channel response transmitted by the phased array antenna to user k in step (1) is represented as:
Figure FDA0003011303180000011
wherein, therein
Figure FDA0003011303180000012
Due to the doppler shift caused by the satellite movement,
Figure FDA0003011303180000013
for propagation delay, gkIs the coefficient of the gain of the channel,
Figure FDA0003011303180000014
is the downlink response vector of the phased array antenna.
3. The method for energy-efficient intelligent dynamic beamforming for multi-beam satellites according to claim 2, wherein in step (2), the objective function is established as
Figure FDA0003011303180000015
Wherein R issumSum of information rates for K users, PsumTotal energy consumption, P, for low-earth satellite systems0Representing the basic power consumption, w, of each userkRepresents the power vector of the phased array antenna to the kth user, the superscript H represents the conjugate transpose, xi represents the constant of the inefficiency of the power amplifier and xi > 1,
Figure FDA0003011303180000021
for the received sir for the kth user in the downlink transmission,
Figure FDA0003011303180000022
the variance of the noise received for the kth user.
4. The method of energy-efficient intelligent dynamic beamforming for multi-beam satellites of claim 3, wherein the following objective optimization problem is established
Q1:
Figure FDA0003011303180000023
Figure FDA0003011303180000024
Wherein P isnFor maximum allowed transmit power for a single antenna, gammakIs the target signal-to-interference-and-noise ratio of the kth user, K is the total number of users, NT＝Mx×MyNumber of antennas of satellite antenna array, MxAnd MyThe number of x-axis and y-axis in the antenna array is respectively, and n represents the serial number of the sub-antenna in the antenna array.
5. The method for energy-efficient intelligent dynamic beamforming suitable for multi-beam satellites according to claim 4, wherein the solution of the optimization problem of step (4) preferably comprises:
a. using semi-positive definite relaxation, define hkThe autocorrelation matrix is
Figure FDA0003011303180000025
wkThe autocorrelation matrix is
Figure FDA0003011303180000026
wiThe autocorrelation matrix is
Figure FDA0003011303180000027
Converting optimization problem into Q3:
Figure FDA0003011303180000028
Figure FDA0003011303180000029
Wherein Tr (·) represents a trace of the matrix;
b. the numerator of the above numerator is represented as A (W), the denominator is represented as B (W), and the numerator part A (W) is obtained by decomposing according to the property of log function:
Figure FDA00030113031800000210
order to
Figure FDA0003011303180000031
Both with respect to WkAccording to the characteristics of the convex programming difference problem, the molecular part A (W) is converted into a concave function by using a Minorize-Maximization iterative algorithm:
Figure FDA0003011303180000032
c. then, carrying out secondary transformation on the whole fraction, and converting the problem into a standard convex optimization problem:
Q4:
Figure FDA0003011303180000033
Figure FDA0003011303180000034
and solving the convex optimization problem with the initial feasible point, continuing iteration for the next time, converting the problem into an iterative optimization problem, and solving an optimal solution.
6. The energy-efficient intelligent dynamic beamforming method for multi-beam satellites according to claim 5, wherein the step (5) of redistributing power by using a Gaussian randomization method comprises:
a. if the rank of the optimal solution is one, performing eigenvalue decomposition on the solved optimal solution matrix to obtain a beam forming vector
Figure FDA0003011303180000035
Wherein v iskAnd ukAre respectively
Figure FDA0003011303180000036
The principal eigenvalues and the eigenvectors of (a).
b. If the rank is not one, converting the optimization problem into a convex optimization problem by using a Minorize-Maximization iterative algorithm again for a plurality of Gaussian randomization processes, and selecting a power distribution vector corresponding to the optimal solution from the obtained Gaussian randomization results to further obtain a final dynamic beam forming vector.
7. The energy-efficient intelligent dynamic beamforming method for multi-beam satellites according to claim 6, wherein in step (6), in solving the allocated power, a convolutional neural network framework is constructed, which comprises an input layer, a convolutional layer, a batch normalization layer, an activation layer, a flat layer, a full connection layer and an output layer, wherein the input is a channel vector
Figure FDA0003011303180000037
And the optimal solution W under the semi-positive definite relaxation conditionoptSplitting a channel vector into a real part and an imaginary part as input; outputting the distributed power p, namely obtaining the mapping relation which can be expressed as
Figure FDA0003011303180000038
Therefore, an iterative process can be replaced, and a final dynamic beam forming vector is obtained.
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CN113765553A (en) * 2021-09-09 2021-12-07 东南大学 Multi-beam satellite communication system robust precoding method based on machine learning
CN114172551A (en) * 2021-12-02 2022-03-11 西安交通大学 Safe transmission method and system based on satellite opportunistic scheduling and combined beamforming
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